Optimization Problem:

Consider the following Branch and Bound tree for a maximization integer programming (IP) model. The objective function of the IP model is 2x1x2+x3. The numbers in the boxes show the optimal solution of the corresponding linear programming relaxation. Answer the following questions. a. From Node 1, what is the information that you can gain about the original IP problem? b. What is the value of the best upper bound that you can obtain for the IP from the figure above? Explain. c. What is the value of the best lower bound that you can obtain for the IP from the figure above? Explain. d. Suppose that you decided to branch on Node 5 with x3. Which inequalities would you add? What can you say about the new sub-problems? e. Is it possible that an optimal solution can be obtained if we branch on Node 4